Notions of Thermodynamics | Bioenergetics

The following points highlight the three important notions of thermodynamics. The notions are: 1. Free Energy Change 2. Application to Chemical Reactions 3. Application to Reactions in Living Organisms.

Notion # 1. Free Energy Change:

If we consider a system consisting of two compounds A and B which react to give C:

A + B → C

By reacting, the system can exchange work or energy (heat, light) with the immediate surroundings. For example, it can receive energy and produce an equivalent work.

At the time of mixing, A + B represent the initial state and C, the product formed, represents the final state.

Each of these 2 states is characterized by an internal energy level (U₁ and U₂ respectively) which depends on the chemical nature of the constituents (with their atoms, their bonds), their concentrations and their position in space (absolute temperature T, pressure P, Volume V…).

The internal energy change, denoted ∆U, resulting from a change of molecular structures (new bonds and different distribution of electrons), depends only on the initial state and final state: ∆U = U₂ – U₁. It is the maximum quantity of energy which can be made available to accomplish a work by the transformation A + B into C. For a constant pressure system (as in the case of many biological reactions) there can be volume changes and either a liberation or an absorption of heat.

The work done by pressure is equal to P (V₂ – V₁), i.e. P∆V. The heat of reaction first defined by ∆Q is equal to the internal energy change plus the work done

∆Q = ∆U + P∆V

If we write H (abbreviation of “heat content”) instead of Q (quantity of heat), the above expression becomes:

for a given temperature, because we know that PV = nRT (n = number of moles, R = gas constant, T = temperature in degrees Kelvin)

∆H is the enthalpy change of the system. ∆H like ∆Q is mostly expressed in cal. or kcal/mole but ought to be expressed in joules/mole (1 calorie = 4.18 joules).

∆H can be measured in a calorimeter. If ∆H < 0 the reaction is exothermic (heat is liberated) and if ∆H>0 the reaction is endothennic (the system ab­sorbs heat). In the past, it was thought that the knowledge of the sign of ∆H is sufficient to predict whether a reaction is spontaneous or not, and it was said that an exothermic reaction is spontaneous while an endothermic reaction is not.

It was then found that while these predictions are correct in most cases, there are exceptions, and that some spontaneous reactions are in fact accom­panied by absorption of heat by the molecules.

One was therefore led to consider the entropy of the system denoted S, a function which measures the disorder of a system, and the variation of which, ∆S = S₂ – S₁, depends — like ∆U — on the initial state and the final state. In order to pass from a first stable state, the initial state, to a new stable state, the final state, one must upset the structures of molecules A and B for the reaction to take place.

The greater the increase in molecular disorder, the greater the entropy (for example, entropy increases while passing from a given protein to the constituent amino acids in free state).

Entropy is related to the complexity of the molecule. The larger the number of atoms, the larger the number of complicated chemical groups, the larger the number of possible structures and the greater the entropy. In a reversible transformation at constant pressure, ∆Q = TAS.

One can then write:

∆G or the free enthalpy change of a constant pressure system is therefore the maximum energy utilizable to accomplish a work. All of the ∆H or heat of reaction is not utilizable. The larger the entropy factor, the smaller the ∆G.

When a reaction proceeds from the initial state to the equilibrium state, free energy may be:

(i) Either converted into heat (in this case AS can be equal to zero);

(ii) Or, used for increasing entropy (in this case ∆H can be equal to zero, which explains that some spontaneous chemical reactions are not accompanied by heat liberation).

Writing ∆U + P∆V for ∆H:

In a reversible transformation at constant volume (∆V = 0) the free energy change is:

In biochemistry, it may be admitted that in most cases ∆V = 0 because the volume changes for reactions taking place in solution are negligible. In equa­tion (3) giving ∆G, it is therefore admitted that P∆V = 0, so that ∆G becomes, like ∆F (equation 4), equal to ∆U – T∆S and therefore ∆F becomes ∆G. This is particularly true if the reactions involve liquids and solids in solution (and no gas) at physiological temperatures which are low.

Three cases are possible. When ∆G < 0, the reaction is exergonic (it can be spontaneous) and free energy is available. On the contrary if ∆G > 0, the reaction is endergonic; free energy must be supplied to the system for the reaction to take place. The reaction will take place only coupled with another exergonic reaction whose negative ∆G is greater in absolute value than the positive ∆G of the endergonic reaction.

Many biochemical reactions are reversible. ∆G = 0 when dynamic equilibrium is reached. This is very interest­ing because for very small variations of active masses of the reaction’s par­ticipants, the reaction can take place in either direction without energy problem as ∆G will vary in either direction.

It may be noted that if ∆S is small, as T is comparatively low in biochemistry, the term T∆S can be neglected and then ∆G = ∆H (see equation 2); in other words, in this case, the terms “exothermic” and “exergonic” on the one hand, and ‘endothermic” and “endergonic” on the other, are similar.

Notion # 2. Application to Chemical Reactions:

If we consider 2 compounds A and B in solution at 25°C under a pressure of 1 atmosphere, each in a concentration of 1 mole/litre of solvent (1 molal) and which can react completely giving C + D (which will therefore be present in the same concentration after total transformation) the free energy change is called “standard” and denoted ∆G₀.

If ∆G₀ < 0, the reaction is exergonic; it can take place spontaneously, but this is not necessarily the case even if the free energy change is very large. In fact, ∆G₀ expresses the free energy change between an initial state and a final state. However, ∆G₀ gives no information on reaction velocity.

A catalyst, an enzyme for example, might be needed to trigger the reaction and adjust its velocity without altering its thermodynamic charac­teristics. Despite the highly negative value of ∆G₀ (-686 kcal/mole) of the total oxidation reaction of glucose (C₆H₁₂O₆ + 6O₂ →  6CO₂ + 6H₂O), this substance can be left for years in presence of the oxygen of air without any oxidation taking place.

On the one hand, while ∆G₀ indicates a standard state, it does not take into consideration the special circumstances which may prevail, particularly in a biological medium: concentration and activities of compounds, pH etc. Nor­mally reversible reactions proceed up to the equilibrium state and ∆G takes this equilibrium state into account.

But the reaction can proceed up to com­pletion if the normal equilibrium state is continuously broken because the reaction products are progressively consumed by a following reaction. This is what happens in metabolic chains where, in fact, a general state of equilibrium is observed.

On the other hand, reactions which, at the limit, can be reversible in vitro can be irreversible in vivo because of metabolic conditions.

Actually, the free enthalpy change ∆G or free energy change ∆F will always depend on metabolic circumstances and will be related to equilibrium states in vivo.

It was indicated that:

∆G₀ depends on the equilibrium constant K of the reaction:

∆G₀ = -RT In K

and that in given circumstances, the effective ∆G of a reaction is:

for a reversible reaction A + B C + D proceeding from left to right. The ∆G of the reverse reaction will have the opposite sign.

Therefore, 2 factors define ∆G, on the one hand, the ∆G₀ which characterises a given reaction, and on the other hand the second factor, characteristic of given circumstances and hence related to concentration, activity, dissociation or protonation of the reaction participants etc. When the ratio of activities of the 2nd factor becomes equal to 1, the 2nd factor becomes zero and ∆G = ∆G₀.

It must be noted that ∆G and ∆G₀ correspond to pH = 0 and ambient temperature while ∆G’ and ∆G₀‘ represent the values in the physiological conditions (pH near 7 and physiological temperature, 30 to 37°) to be specified in each case.

Let us examine the case of a reaction whose ∆G₀ = -3 kcal/mole. It is known that R = 1.987 cal/mole/degree, that at 25°, T = 273 + 25 = 298°K and that In K = 2.30 log K. We can write:

∆G₀ = -3 000 cal/mole = -1.987 x 298 x 2.30 log K = -1362 log K

therefore,

log K = -3 000/ -4362 = 2.2

i.e., approximately equal to 2, which corresponds to a value of K equal to about 100.

But it was indicated that K = , therefore [C][D] = 100 [A][B], which means that at equilibrium, transformation of A + B into C + D would have been almost total (99%).

If on the contrary, a reaction has a ∆G₀ = + 3 kcal/mole, then K will be approximately equal to 0.01, in other words, the reaction will practically not take place because equilibrium will be reached as soon as only 1% of the reactants will have been transformed.

It follows that the ∆G₀ of a reaction can be calculated if one knows K, i.e., if one can measure the concentrations of the reactants and reaction products (this is possible, except when K is extremely small or extremely large because then the concentrations of the reaction products or reactants are too low to be determined accurately). Figure 3-1 gives the values of ∆G₀ for a series of values of K from 10^-3 to 10⁶.

It is clear that the reactions whose equilibrium constant is > 1 are accom­panied by a decrease of free energy (this energy becomes available); these are exergonic reactions. On the contrary, if K is < 1, the reaction is endergonic.

Notion # 3. Application to Reactions in Living Organisms:

The ∆G’ in given conditions will define the direction of the reaction (and not the ∆G₀ or the ∆H).

Since ∆G’ = ∆G₀ + RT In and since ∆G₀ is a constant for a given system which can be found in tables, it is the 2nd circumstantial factor which will decide the direction of the reaction. This is why one often indicates an interval of ∆G’ values which a reaction can take in normal physiological conditions.

For example, the energy yielded by the cleavage of ATP to ADP + P_i can have a ∆G’ between 7 and 12 kcal/mole in physiological conditions. The reactions close to equilibrium can proceed sometimes in one direction, some­times in the other.

When products are eliminated from the system as and when they appear (CO₂ for example or by another reaction) equilibrium is displaced in the same direction.

Moreover, even a reaction having a largely positive ∆G₀, can take place in living cells when it is part of a sequence of reactions and when the ∆G of the whole pathway is < 0; the products of this reaction will be continuously taken over by the following reaction, so that despite its theoretically unfavourable equilibrium, the reaction with ∆G > 0 can continue to take place, because in fact its ∆G becomes negative as the products are continually consumed.

Lastly, one can consider at this juncture, the problem of the synthesis of macromolecules such as polyosides or proteins; the ∆G for the polymerization of oside units into polysaccharides or for the polymerization of amino acids into proteins is very largely positive and in this case there is no following reaction which takes over the products formed, because they are terminal products.

Indeed, despite the unfavourable equilibrium, there could still be synthesis of polysaccharides or proteins in small quantities if there were very high con­centrations of monosaccharides or amino acids; but precisely the reverse situation prevails in living cells: the concentration of polymers is very high compared to that of monomers (glucose and free amino acids).

It must be concluded that the polymers are not formed by simple polymerization of monomers and we will see that indeed, the macromolecules (polysaccharides, proteins, nucleic acids) are synthesized by different processes in which the global free energy change is negative.

The example of polysaccharides or proteins is not unique; it may be said generally, that living cells are far from being systems in equilibrium. The creation and maintenance of such a situation require energy from the environ­ment of the cell; if the external source of energy disappears and consequently energy transfer to the cell is no longer possible, the cellular processes will all tend towards equilibrium: the cell dies.

Once energy has been absorbed by the living cell — in the form of light or chemical substances — energy transfers are necessary to permit the synthesis of biochemical compounds like polysaccharides, nucleic acids or proteins. We have already mentioned the fact that in living organisms, thermal energy is not a possible intermediate.

The living cell cannot therefore be compared with an internal combustion engine where the chemical energy of molecules is partly transformed, during the combustion (oxidation) of petrol, into kinetic energy (heat) which causes the expansion of gases and thereby the movement of a piston (mechanical energy). Cells do not use this type of energy transfers for their endergonic reactions and it must be noted that an increase of temperature would rapidly cause the denaturation of proteins, particularly enzymes.

Indeed, the cells do call upon the oxidation of some substances, but contrary to what happens in an internal combustion engine, cellular oxidations take place without great changes of either temperature or pressure.

It is true that a part of the energy is liberated in the form of heat (and this enables the homeotherms to maintain their temperature constant), but this fraction of energy is no longer available for performing the endergonic reactions. In fact, the major part of the energy remains in the chemical form and it is transferred directly from one molecule to another.