Introduction and Goals
In this tutorial we will discuss the principles governing the transformation of energy, also known as thermodynamics. In particular, we will focus on how thermodynamics applies to the energy generated and consumed by a cell. Cells are in a constant state of flux, with many processes and reactions that either consume or generate energy. We will examine how the laws of thermodynamics can be used to predict the likelihood of any given process or reaction, and determine the amount of energy released or required.
By the end of this tutorial you should know:
- The first and second laws of thermodynamics
- The concepts of enthalpy and entropy
- The concept of thermodynamic spontaneity
- Free energy (G) and how it can predict the likelihood of a reaction
- The meaning of the standard free energy change (deltaGº')
- How to relate the standard free energy change (deltaGº') to the equilibrium constant (Keq)
- How to relate the standard free energy change (deltaGº') to the free energy change for prevailing conditions
Forms of Energy
A hallmark of a living cell is the ability to both use and generate energy. Energy(E) is commonly defined as a system's ability to do work. Stated differently, energy has the ability to change or move something. In the context of living organisms, energy is needed to do work. This includes synthetic work (the ability to generate new molecules), mechanical work (the ability to move the position of a cell, or some part of it), work against a gradient (the ability to move molecules against a concentration gradient), and work that generates heat (the ability to maintain a constant body temperature). Cells constantly undergo changes in response to their environment and their normal growth.
In most cases, energy is released by the breaking of chemical bonds. For example, C6H12O6 + 6O2 -> 6 CO2 + 6H2Odescribes the complete oxidation of glucose. Bonds are broken to generate energy that the cell can use, usually in the form of ATP. Energy exists in two alternate states: kinetic energy and potential energy. Kinetic energy refers to the energy of motion. Potential energyrefers to stored energy poised to do work. The animation is a cartoon analogy of potential and kinetic energy. The spring, when it is coiled and poised to spring, has potential energy (i.e. energy to move the frog). The release of the spring provides kinetic energy (i.e. energy to make the frog jump). Let's also consider the following two examples of potential energy. Potential energy is stored in the chemical bonds between the phosphates in ATP. When cleaved, energy is generated. Potential energy is also stored in a concentration gradient; that is, the difference in concentration of a substance across a membrane (e.g. the difference in sodium concentration on either side of the plasma membrane). The potential energy stored in a concentration gradient is the potential for work; in this case, the movement of substances across a membrane. This will become clear in subsequent tutorials discussing diffusion and transport (Membrane Structure and Function and Passive and Active Transport) .
The First Law of Thermodynamics
Thermodynamics is a discipline of physical chemistry that defines the laws that govern energy transformations. Thermodynamics deals with the energy transformations in the universe, between a system and its surroundings. Bioenergetics is the application of thermodynamics to biological systems. In this context, the cell is the system and the rest of the universe is its surroundings. Furthermore, a cell is an open system, defined by its ability to exchange energy with its surroundings. The exchange of energy between a system and its surroundings is in the form of either work or heat. For most cells, there is only a small amount of heat released and the bulk of energy is applied to work. The first law of thermodynamics states that the total amount of energy in the universe is constant. Therefore, for the universe as a whole, energy is converted from one form to another, but it is not created or destroyed. For any open system, the amount of energy in the system, termed the internal energy, equals the amount of energy coming into the system from the surroundings minus the amount of energy released by the system into its surroundings:
A change in internal energy after a system undergoes some process is referred to as deltaE, and deltaE can be measured as the difference in internal energy after the change minus the internal energy before the change (deltaE = Eafter - Ebefore). For any given chemical reaction, the change in internal energy equals the internal energy of the products minus the internal energy of the reactants. Remember that energy is not lost or generated, but it is converted to another form, often heat transferred to the surroundings:
Under conditions of constant pressure and volume, which is generally the case for biological systems, the change in internal energy is approximately equal to the change in enthalpy (deltaH), which is a measure of bond energy or total energy of a system:
If the value of deltaH is negative, the process is exothermic and energy is liberated, usually as heat. If the value of deltaH is positive, the reaction is endothermic and energy is required. Most biological processes and reactions are reversible. Consider the oxidation of glucose (C6H12O6 + 6 O2 -> 6 CO2 + 6 H2O). The reverse reaction, 6 CO2 + 6 H2O -> C6H12O6 + 6 O2, describes the process of photosynthesis. Oxidation of glucose is an exothermic reaction, resulting in the release of energy. Photosynthesis is an endothermic reaction, requiring an input of energy from the surroundings in the form of sunlight.
The Second Law of Thermodynamics
As described above, most biological processes are reversible. In some instances we have an intuitive feeling for the direction of the process. For example, when you drop a sugar cube into a glass of water you know that the sugar will eventually dissolve, and you also know that it is very unlikely that the dissolved sugar will spontaneously reform into a sugar cube. However, for most reactions it is difficult to predict if the forward or reverse reaction is likely to occur. Knowing the change in enthalpy (deltaH) of a reaction does not help predict the direction of a reaction because the first law of thermodynamics states that energy is always conserved, and there is no inherently favored direction to the transfer of the energy. The second law of thermodynamics is more useful in predicting the direction and likelihood of any given process. The second law of thermodynamics states that events that are likely to happen are those that increase the randomness or disorder in the universe. Restated, a thermodynamically favored process is one that increases the dispersal of energy in the universe. The measure of this change in the universe is referred to as the change in entropy (deltaS). Referring back to the example of the sugar cube, the sugar cube dissolving in the water results in an increase in entropy (+deltaS) because the sucrose molecules disperse throughout the glass of water, as opposed to the regular and ordered array of sucrose in the sugar cube. Therefore, the sugar cube dissolving in water is a thermodynamically favored process. Restated, the dissolution of the sugar cube is a spontaneous process. In the context of thermodynamics, a spontaneousprocess does not mean it will occur instantaneously; rather, this means it is likely to occur. It is not a measure of the rate of the reaction.
At first glance it would seem that the very basis of life, the cell, defies the second law of thermodynamics. Clearly, the cell is a highly organized structure, composed of many ordered components and processes, each of which appears to reduce the entropy of the cell. How can we explain this contradiction? The second law of thermodynamics states that for every spontaneous process, the entropy of the universe must increase; the entropy of the universe (deltaS universe) is composed of the entropy of the system (deltaS system) plus the entropy of the surroundings (deltaS surroundings):
Therefore the deltaS of the system (e.g. a process or reaction) can decrease as long as it is accompanied by a greater increase in the deltaS of the surroundings, resulting in an overall increase in deltaS of the universe. Determining the likelihood of any process is dependent on knowing how that process changes the entropy of the universe.
J. Willard Gibbs, a chemist, defined a concept of free energy(the energy available to do work) that is the most useful measure of thermodynamic spontaneity. Initially Gibbs defined the equation:
The change in enthalpy (deltaH) of a reaction is equal to the change in free energy (deltaG; available or required) plus the change in entropy (deltaS) multiplied by the absolute temperature in Kelvin units (T). In systems of constant pressure and volume, the value TdeltaS is the amount of energy dispersed and unavailable for work.
The equation can be rearranged to calculate the change in free energy:
Favored processes are ones that go toward a lower free energy (negative deltaG values). Processes with a negative deltaG are exergonic (spontaneous and generate available free energy). Processes with a positive deltaG are endergonic(energy is required); they will not occur under their current conditions. This does not mean that the process will never occur, but it will require the input of free energy. At this point it is worth reiterating that an exergonic process, which is thermodynamically favored and spontaneous, will not necessarily happen. Thermodynamic spontaneity is a measure of the likelihood of a process and the amount of free energy generated, but not the rate of the process.
As the equation for deltaG is written, it appears that favored processes (-deltaG) will tend toward a lower enthalpy (-deltaH) and a higher entropy (+deltaS) of the system. This is, in fact, misleading; the driving force is the increase of entropy in the universe. The free energy equation describes the likelihood of a process as a function of the change in the entropy of the universe, expressed as the sum of the change of entropy in the system (deltaS) and the change of entropy in the surroundings (-deltaH/T). A process can be thermodynamically favored (-deltaG) even though it proceeds toward higher enthalpy (deltaH), as long as it is associated with an increase in entropy and the value of TdeltaS is greater than deltaH. Alternatively, a reaction can proceed even though there is a decrease in entropy of the system (-deltaS), as long as there is a significantly larger decrease in enthalpy (-deltaH).
Free Energy and Reversible Chemical Reactions
All chemical reactions are reversible, and the change in free energy (deltaG) determines the direction of the reaction. Consider the reaction:
A thermodynamically favored reaction goes toward a state of lower free energy, so the deltaG value is negative. If the deltaG for the forward reaction has a negative value, then the reaction A + B -> C + D is favored. If the deltaG has a positive value, then the reverse reaction C + D -> A + B is favored. The change in free energy of a reaction is a measure of how far a reaction is from equilibrium and the amount of free energy that will be available or required when it reaches equilibrium. It should be pointed out that the reaction will always go in both directions, forward and reverse; however, the deltaG value will determine which direction is favored, and therefore, will result in accumulation of either products (C + D) or reactants (A + B).
All chemical reactions will go toward equilibrium, defined as the point at which the rate of the forward reaction is equal to the rate of the reverse reaction. The equilibrium constant (Keq) is the ratio of the concentrations of products and reactants at equilibrium. The change in free energy (deltaG) is a measure of the free energy available or required as the reaction approaches equilibrium. At equilibrium, there is no available free work and deltaG = 0. The change in free energy is a measure of how far a reaction is from equilibrium, and therefore, is a function of the concentrations of reactants and products at the start of the reaction. Assume the conditions for the reaction above (A + B -> C + D) are such that the ratio of products to reactants ([C][D] / [A][B]) is 2. The Keq for this reaction is 10. Therefore, this reaction is likely to go in the forward direction to generate more C and D. If the conditions are such that the ratio of products and reactants are 20, then the reaction is likely to go in the reverse direction to generate more A and B. This is illustrated graphically in Figure 1.
Standard Free Energy Change and Keq
Given that the change in free energy (deltaG) is related to the concentrations of reactants and products at the start of a reaction, one would need to calculate the deltaG for every possible condition. In order to simplify the calculation of deltaG, biochemists have established the standard free energy change (deltaGº') as the change in free energy for a reaction under standard uniform conditions, defined at a constant temperature (25ºC), constant pressure (1 atm) and neutral pH (7.0), with all reactants and products at a 1M concentration. deltaGº' is a measure of the available free energy (or conversely, the free energy required) as the reaction proceeds from the defined standard conditions to equilibrium. One can use deltaGº' to determine the deltaG of a reaction under any condition by using the following equation, which relates changes in free energy (deltaG) to the concentrations of products (C + D) and reactants (A + B) at prevailing (prev) conditions.
The prevailing concentrations of reactants and products will be different than the standard conditions of 1M reactants and products (which are simply arbitrary assignments). R is the gas constant (1.987cal/molK) and T is absolute temperature (ºK). While deltaGº' is a useful term to define, the actual free energy of a reaction is dependent on the concentrations of reactants and products for the specific conditions being considered. In fact, some reactions have a positive deltaGº' but can be spontaneous under some conditions. In these cases, the value of RTln[C]prev[D]prev/ [A]prev [B]prev is less than -deltaGº'.
Using this equation, one can relate deltaGº' directly to the Keq. Assume that the reaction A + B -> C + D is at equilibrium; therefore, deltaG = 0 and [C]prev [D]prev / [A]prev [B]prev = Keq. Once these values are substituted, the equation to express deltaG as a direct function of Keq can be rewritten as:
0 = deltaGº' + RTlnKeq
Therefore the standard free energy change (deltaGº') of a reaction, the free energy available as the reaction proceeds from standard conditions toward equilibrium, is proportional to the Keq. If the Keq is greater than one, then at equilibrium products predominate over reactants and deltaGº' has a negative value. This means that a reaction at standard conditions, where [products]/[reactants] = 1, will proceed in the forward direction and generate more product. Alternatively, if the Keq is less than one, then at equilibrium reactants predominate over products and deltaGº' has a positive value. In this case, a reaction at standard conditions will proceed in the reverse direction and generate more reactants. Finally, if the Keq is equal to one, then the concentrations of products and reactants are equal; therefore, a reaction at standard conditions is already at equilibrium and deltaGº' equals zero. The relationship between Keq and deltaGº' is illustrated in Figure 2.
Coupling Exergonic and Endergonic Reactions
We have defined deltaG as a measure of the likelihood that a reaction will proceed, and stated that exergonic reactions with -deltaG values are thermodynamically favored. This seems to suggest that the reverse reaction, which is endergonic, will never occur; however, this is not the case. The endergonic reaction can occur if sufficient free energy is applied. This is accomplished in a cell by coupling two separate reactions: an endergonic reaction and an exergonic reaction. The free energy of the exergonic reaction is used to drive the endergonic reaction. Often, ATP hydrolysis, which is exergonic, is coupled to an endergonic reaction. For example, the first reaction in glycolysis, the pathway of glucose metabolism, is the phosphorylation of glucose:
Glucose + Pi (inorganic phosphate) -> Glucose-6-P + H2O
deltaG°' = +3.3 Kcal/mol
This is coupled to ATP hydrolysis:
ATP + H2O -> ADP + Pi
deltaG°' = -7.3 Kcal/mol
The coupled reaction is:
Glucose + ATP -> ADP + Glucose-6-P
deltaG°' = -4.0 Kcal/mol
The coupled reaction is exergonic and thermodynamically favored.
We have demonstrated that the change in free energy is a measure of how far a reaction is from equilibrium and the energy available for work as the reaction proceeds toward equilibrium. In isolation, all reactions will eventually reach equilibrium, at which point deltaG = 0 and there is no free energy available. Reactions in a cell, however, are not isolated and rarely reach equilibrium. Instead, cells maintain most reactions in a steady state (relatively constant concentrations of reactants and products) that is usually far from equilibrium. This is achieved through constant replenishment of reactants and depletion of products. Reactions in a cell do not exist in isolation; often, they are part of large interconnected networks of chemical reactions, so that the products of one reaction are often the reactants of another. Furthermore, some cells (photosynthetic cells) can interact with their environment and receive energy from their surroundings in the form of sunlight, and others can obtain energy from organic molecules such as sugars and lipids.
The first two laws of thermodynamics govern the transformations of energy (E) in the universe. There are two forms of energy: potential energy and kinetic energy. The first law of thermodynamics states that the energy of the universe is conserved. The change in energy of a system, defined as the change in enthalpy (deltaH), can be negative or positive. However, the energy in the universe cannot be generated or lost; rather, it is transformed from one state into another. Reactions with a -deltaH are exothermic and release energy. Reactions with a +deltaH are endothermic and require energy to proceed. The second law of thermodynamics states that the dispersal of energy, or disorder, in the universe is always increasing. The measure of disorder is the change in entropy (deltaS ). The free energy equation incorporates both changes in enthalpy and entropy, and provides a measure for the amount of free energy available for work that is generated or required when a reaction proceeds. The free energy equation is deltaG = deltaH - TdeltaS. Negative deltaG values indicate a spontaneous and exergonic reaction, which generates free energy. Positive deltaG values indicate an endergonic reaction, which will occur only with an input of free energy. For reversible reactions, the sign of deltaG indicates the direction of the reaction; a deltaG < 0 indicates that the forward reaction is favored, whereas deltaG > 0 indicates that the reverse reaction is favored. At equilibrium, the rates of the forward and reverse reactions are the same and deltaG = 0, indicating that no free energy is generated or required. deltaGº' represents the standard free energy change, assuming a set of standard conditions of temperature, pH, and concentrations of products and reactants. deltaGº' is related to Keq, and can be calculated from the equation deltaGº' = -RTln Keq. The free energy under prevailing conditions can be determined by using deltaGº' in the equation deltaG = deltaGº' + RTln [products]/[reactants]. deltaG is a measure of how far a reaction is from equilibrium and the available free energy generated as it proceeds toward equilibrium. Endergonic reactions can occur if they are coupled to exergonic reactions, which provide free energy. In cells, most reactions never reach equilibrium and are maintained in a steady state.