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# Bai 3

Module by: Thang Nguyen. E-mail the author

Internal Energy (E)

The internal energy of a biochemical system includes any kind of energy that might be changed by any chemical or biochemical reaction. Examples include the kinetic energy of motion and the energy of vibration and rotation of every atom, molecule and ion in the system. Other examples include all of the energy stored in the chemical bonds between atoms and the energy of noncovalent interactions between molecules and ions. The internal energy of a system is a function of its state. That is, the internal energy depends only on the initial and final states of the system, not on the path taken to get from the initial state to the final state. The thermodynamic state of a system is defined by prescribing the amounts of all substances and any two of the following three system variables:

1) Temperature (T)

2) Pressure (P)

3) Volume (V)

An open system can exchange energy with its surroundings and may therefore change its internal energy. This change is called

E. Internal energy exchanges can only involve heat (q) or work (w). This is the first law of thermodynamics: E = q-w, where a positive value of q indicates heat absorbed by the system from its surroundings and a positive value of w indicates work is done by the system on its surroundings. Conversely, a negative value of q means that heat flows from the the system to its surroundings and a negative value of w means that the surroundings do work on the system.

When V is changed against a constant P, w = P

V or, using the ideal gas law,

w=

nRT.

Enthalpy

The enthalpy (H) is defined as H = E + PV. Where E is the internal energy, P is the pressure, and V is the volume.

At constant pressure,

H = E + PV. The same result can be obtained from the first law of thermodynamics:

E = q-w, so

q =

E + w, but w = PV when V is changed against a constant P, so

q =

E + PV

Thus, when the heat of a reaction is measured at constant pressure, it is really

H that is measured. Furthermore, most biological processes occur at constant pressure, so H gives a more accurate measure of the energy available from a biological process than E does. Finally, because E and PV are functions of state (not path), H is also a function of state. Thus, H depends only on the initial and final states of the process for which it is calculated.

Entropy and the Second Law of Thermodynamics

E and H describe the energy changes, but tell nothing about the favored direction for a process. To do this, one must take into account the degree of randomness or disorder of a system. The degree of randomness or disorder of a system is measured by a state function called the Entropy (S). Entropy is defined as S = kln(W), where k is the Boltzmann constant (the gas constant R divided by Avogadro's number) and W is the number of thermodynamic substates of equal energy.

The entropy of an ordered state is lower than that of a disordered state of the same system. For example, there are more ways to put a large number of molecules in a random or disorderly arrangement than there are to put them in an orderly arrangement. Thus, the increasing entropy in a system is a thermodynamic driving force.

The second law of thermodynamics states that the entropy of an isolated system will tend to increase to a maximum value. However, this form of the second law is of little use biologically because it applies only to isolated systems (systems that do not exchange energy with their surroundings). Most biological systems, however, are open - they exchange energy and matter with their surroundings. Thus, biological systems undergo changes in energy and entropy in many reactions, and both must determine the direction of thermodynamically favorable processes. The Gibbs Free Energy (G) is a function of state that includes both energy and entropy terms:

G = H-TS, where T is the absolute temperature, H (the enthalpy) measures the energy change at constant pressure, and S (the entropy) measures the randomness of the system. At constant temperature and pressure,

G = H -TS

A decrease in energy (-

H) and/or an increase in entropy (+S) tends to make a process favorable. Either a negative H or a positive S tends to make G negative. Thus, the second law can be restated for open systems as follows:

1.

G must be negative for a process in an open system to be favorable at constant temperature and pressure.

2. A positive

G indicates a process is not favorable.

Interplay of Enthalpy and Entropy

Table 3.3 summarizes how the balance between enthalpy and entropy determines the direction in which a process is thermodynamically favorable. However, keep in mind the following:

1. The favorability of a process (negative

) has nothing to do with reaction rate.

2. The entropy of an open system can decrease, but energy must be expended to do so, however.

Table 3.3

Free Energy and Useful Work

The term

represents the portion of an energy change (H) that is available to do useful work. If H is the total energy in a reaction, then G = H -TS indicates that part of H is alway dissipated as heat (the TS term) and is therefore unavailable for other things, such as muscle contraction, ion transport, or tissue growth. The remaining amount () is available for useful work, but may not actually be fully utilized for useful work because the efficiency of a process (the ratio of work actually accomplished to , the maximum work available) is always less than 100%.

Free Energy and Concentration

Standard state represents a 1M solution. The chemical potential of a component A (GA) is equal to the chemical potential at the standard state plus RT ln[A]

At [A] = 1M, GA = GA

Consider moving molecule A from one side of a membrane through which A can pass (region 1) to the other (region 2).

The free energy of moving A out of region 1 is given by

The free energy of moving A into region 2 is given by

Overall,

Thus, if the concentration of A in region 2 is lower than in region 1,

G is negative and the process is favorable. On the other hand, if the concentration of A in region 2 is higher than in region 1, G is positive and the process is unfavorable

Free Energy Change and the Equilibrium Constant

Free energy is a state function, so

G for a reaction depends only on the free energy of the initial state (the reactants) and the free energy of the final state (the products):

G = G(products) - G(reactants)

Consider the reaction aA + bB <=> cC + dD, where a is the number of moles of component A, b is the number of moles of component B, etc.

Using the equation for the chemical potential, and collecting the standard state terms into a single

, yields

G = + RT ln {([C]c[D]d)/([A]a[B]b)}

Simplifying (and remembering that each product and reactant must be raised to the appropriate power) yields the following general equation for determining

G under any set of conditions, where is the free energy change for the standard state (1M):

G = + RT ln{[Products]/[Reactants]}

At equilibrium, the equilibrium constant K for the reaction is given by

K = {([C]c[D]d)/([A]a[B]b)}

Recall that

G = 0 at equilibrium, so substituting yields

0 =

+ RT ln K,

-

= RT lnK, or

Whenever a system is displaced from equilibrium, it will spontaneously proceed in the direction necessary to reestablish the equilibrium state. Negative

G is the driving force for such a reaction.

Coupled Reactions

Reactions, such as A<=>B and C<=>D, when coupled, have a

that is the sum of the individual s. This may be important if one of the reactions has a fairly large positive .

1. Three important terms relating to the free energy change of a process are:

- the total free energy change for a reaction under any conditions

- free energy under standard conditions (all concentrations of 1M)

, the free energy change under standard biological conditions (all concentrations 1M, [H2O] = constant, and pH = 7.0)

Thus, a positive

may influence a reaction, but cellular conditions may make the overall for the reaction negative.

2.

and only determines whether a reaction is favorable as written.. Only when is negative is a reaction favored. The sign of or does not determine the direction a reaction will proceed.

3.

depends on temperature ( = H - TS). This can be a factor for a given reaction occurring in different organisms living under very different conditions of temperature.

Factors Contributing to Large Energies of Hydrolysis of Phosphate Compounds

1. Resonance stabilization of phosphate products. Figure 3.9 depicts the resonance stabilization of the orthophosphate ion, HPO42- (abbreviated Pi). The multiple resonance forms are of equal energy, but all are not possible when the phosphate group is bound in an ester, such as ATP. Once Pi is released upon hydrolysis, however, the multiple resonance forms increase the overall entropy of the system, an energetically favorable process.

Figure 3.9: Resonance stabilization of orthophosphate, HPO42- (Pi).

2. Additional hydration of hydrolysis products - Release of Pi allows greater opportunities for hydration. Hydration is an energetically favored state.

3. Electrostatic repulsion between charged products - When both products of hydrolysis are negatively charged (e.g., ADP and Pi in the hydrolysis of ATP), repulsion of the ionized products favors hydrolysis.

4. Enhanced resonance stabilization or tautomerization of product molecules - Hydrolysis is favored when product molecules can adopt multiple molecular forms. For example, pyruvate has two molecular forms, whereas PEP has only one.

5. Release of a proton in buffered solution - A proton is released in some hydrolysis reactions (see Figure 3.7), so hydrogen ion concentration (pH) influences the reaction.

For ATP4- + H2O <=> ADP3- + HPO42- + H+,

G = + RT ln {([ADP3-][HPO42-][H+])/([ATP(-4)][H2O])}, which can be rearranged as

G = + RTln { ([ADP3-][HPO42-]) / ([ATP4-])} + RT ln{[H+]/[H2O]}

Because RT ln{[H+] / [H2O]} is relatively constant at pH 7.0 in biological systems, it can be incorporated into

to make . Thus,

= +RT ln{[H+] / [H2O]}

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