Introduction

Calorimetry is the only means by which one can make direct, model-independent measurements of thermodynamic quantities. Spectroscopic techniques, though in many cases extremely sensitive or useful for obtaining high-resolution structure information, can give but an indirect, model-dependent determination of thermodynamic quantities. Calorimetric analysis therefore complements spectroscopic studies, giving a more complete description of the biological system of interest. Modern microcalorimeters are both accurate and sensitive, so that measurements require relatively small amounts of material (as little as 1 nmol) and can yield data of relatively low uncertainty.

Diffuse heat effects are associated with almost all physico-chemical processes. Microcalorimetry provides a way of studying the energetics of biomolecular processes at the cellular and molecular level, and it can be used to determine thermodynamic quantities of conformational change in a biological macromolecule, ligand binding, ion binding, protonation, protein–DNA interaction, protein–lipid interaction, protein–protein interaction, protein–carbohydrate interaction, enzyme–substrate interaction, enzyme–drug interaction, receptor–hormone interaction, and macromolecular assembly. Microcalorimetry is also useful in the analysis of thermodynamics of very complex processes, for example, enzyme kinetics and cell growth and metabolism. Calorimetry is not narrowly applicable to processes occurring at equilibrium.

There are three broad classes of biological calorimetry: bomb calorimetry, differential scanning calorimetry (DSC), and isothermal titration calorimetry (ITC). Other biocalorimeters are usually derivatives of these types. The choice of instrument will ordinarily depend on the process of interest. Bomb calorimetry is used to measure the energy content of foods and other materials; discussion of the technique can be found in Chapters 1 and 2.

Introduction

We have seen that a given amount of energy can be distributed in many different ways – something like how a certain volume of fluid can adopt many different shapes and adapt itself to its container. In this chapter we turn the spotlight on a thermodynamic function that enables us to measure how “widely” a quantity of energy is distributed.

The First Law of Thermodynamics relates heat, work and internal energy, and it tells us that energy is neither created nor destroyed in all its changes of form; the total energy of a reaction, and indeed of the universe, is constant. The First Law tells us with breathtaking generality that a boundary on the possible is a basic characteristic of our universe. It is not hard to see, though, that the First Law does not tell us some things we would like to know. For instance, if we put a “hot” system into contact with a “cold” one and allow them to come to thermal equilibrium, we find that the final temperature of the two objects, which will persist indefinitely if the combined system is isolated, is at some intermediate value. The value of ΔU for this reaction, however, which obviously proceeds spontaneously, is 0. Similarly, if we add a “concentrated” solution of substance A to a “dilute” solution of substance A, we find that the final concentration of the combined system, which will persist indefinitely if the system is isolated, is between the initial concentrations (Fig. 3.1).

Introduction

The foregoing chapters focused on practical and applied aspects of thermodynamics and statistical mechanics. These subjects provide ways of thinking about energy transformation, methods for determining the direction of spontaneous change, the magnitude of thermodynamic quantities when a system passes from one state to another, and the molecular origin of change. Useful as they are, however, thermodynamics and statistical mechanics do not tell us everything we'd like to know: they give no direct indication of the rate at which a chemical change will occur nor how the rate of change will vary with conditions.

The present chapter seeks to bridge some of the gaps which remain from a strictly thermodynamic treatment of topics of interest in biochemistry. It might seem counter-intuitive for this chapter to appear next to last instead of first, since one of the most basic aspects of our experience of the world is change. Plants grow, go to seed, and die, while animals move, eat, reproduce, and die. And the molecules bacteria, plants, and animals are made of are always moving. But the title of this book is Biological Thermodynamics, not Biological Kinetics!

As we have seen, analysis of free energy changes provides a way of answering such questions as “Why is most of the energy of glucose harvested in the citric acid cycle and not in glycolysis?”. But in order to respond well to “Does H2CO3 break down fast enough on its own to permit metabolic CO2 to be excreted into the atmosphere?” we must turn to reaction kinetics.

Introduction

Beginning perhaps with Anaximenes of Miletus (fl. c. 2550 years before present), various ancient Greeks portrayed man as a microcosm of the universe. Each human being was made up of the same elements as the entire cosmos – earth, air, fire, and water. Twenty-six centuries later, and several hundred years after the dawn of modern science, it is somewhat humbling to realize that our view of ourselves is fundamentally unchanged.

Our knowledge of the matter of which we are made, however, has become much more sophisticated. We now know that all living organisms are composed of hydrogen, the lightest element, and of heavier elements like carbon, nitrogen, oxygen, and phosphorus. Hydrogen was the first element to be formed after the Big Bang. Once the universe had cooled enough, hydrogen condensed to form stars. Then, still billions of years ago, the heavier atoms were synthesized by nuclear fusion reactions in the interiors of stars. We are made of “stardust.”

Our starry origin does not end there. For the Sun is the primary source of the energy used by organisms to satisfy the requirements of life (Fig. 1.1). Some organisms acquire this energy (Greek, en, in + ergon, work) directly; most others, including humans, obtain it indirectly. Even chemosynthetic bacteria that flourish a mile and a half beneath the surface of the sea require the energy of the Sun for life.

Introduction

To gain a good understanding of the laws of thermodynamics, it will help to develop an appreciation of the meaning of the words law and thermodynamics. Let's take a moment to think about these words before launching into a detailed discussion of how we might unpack the content of how the laws can be formulated. We are aided in this quest by the nature of science itself, which unlike ordinary prose and poetry aims to give words a more or less precise definition.

We are familiar with the concept of law from our everyday experience. Laws are rules that we are not supposed to break; they exist to protect someone's interests, possibly our own, and there may be a penalty to pay if the one who breaks a law gets caught. Such are civil and criminal laws. Physical laws are similar but different. They are similar in that they regulate something, namely how matter behaves under given circumstances. They are different in that violations are not known to have occurred, and they describe what is considered to be a basic property of nature. If a violation of a physical law should ever seem to have occurred, you will think first that the experiment has gone wrong at some stage, and second that maybe the “law” isn't a law after all.

Here's an example. Galileo, like Copernicus, believed that the orbits of the known planets were circles; the circle being the shaper of perfection and perfection being of the heavens.

Introduction

We have seen how the First and Second Laws are combined in a thermodynamic potential function called the Gibbs free energy. We have also seen how the Gibbs energy can be used to predict the direction of spontaneous change in a wide variety of systems under the constraints of constant temperature and pressure. One type of application of the Gibbs energy, which we studied in Chapter 5, is the binding of a ligand to a macromolecule. And in Chapter 6 we became introduced to statistical thermodynamics, a mathematical formalism that permits a molecular interpretation of thermodynamic quantities. The present chapter combines and extends all these ideas. Binding is a ubiquitous and immensely important general topic in biochemistry. While binding can be considered just one of many different types of equilibrium process, the key role it plays in the physiology of biological macromolecules makes the present chapter one of the most important of the book.

Let's do a brief survey of areas in biology where binding plays a role – before plunging into a sea of mathematical equations. In our discussion of the First Law (Chapter 2) we encountered RNase A, a digestive enzyme that can bind tightly to a nucleotide inhibitor. Then in Chapter 5, we looked at receptor–ligand interactions and an introductory analysis of oxygen binding to hemoglobin. And an exercise in Chapter 5 involved the binding of a regulatory protein to DNA (Fig. 7.1).

Energy value and nutrient content of foods

Physical properties of amino acids

Protonation energetics at 298 K

Buffer ionization constants

Energetics of the reactions of the citric acid cycle

Interest in the biological sciences has never been greater. Today, biology, biochemistry, biophysics, and bioengineering are engaging the minds of young people in the way that physics and chemistry did thirty, forty, and fifty years ago. There has been a massive shift in public opinion and in the allocation of resources for university-based research. Breakthroughs in genetics, cell biology, and medicine are transforming the way we live, from improving the quality of produce to eradicating disease; they are also stimulating pointed thinking about the origin and meaning of life. Growing awareness of the geometry of life, on length scales extending from an individual organism to a structural element of an individual macromolecule, has led to a reassessment of the principles of design in all the engineering disciplines, including computation. And a few decades after the first determination at atomic resolution of the structures of double-stranded DNA and proteins, it is becoming increasingly apparent that both thermodynamic and structural information are needed to gain a deep sense of the functional properties of biological macromolecules. Proteins, nature's own nanoscale machines, are providing inspiration for innovative and controlled manipulation of matter at the atomic scale.

This book is about the thermodynamics of living organisms. It was written primarily for undergraduate university students; mostly students of the biological sciences, but really for students of any area in science, engineering, or medicine.

Adkins, C. J. (1983). Equilibrium Thermodynamics, 3rd edn. Cambridge: Cambridge University Press.

Atkinson, D. E. (1987). Dynamic Models in Biochemistry. Menlo Park: Benjamin.

Bederson, B. (1991). Atoms. In Encyclopedia of Applied Physics, ed. G. L. Trigg, vol. 2, pp. 245–96. New York: VHC.

Bisswanger, H. (1996). Proteins and Enzymes. In Encyclopedia of Applied Physics, ed. G. L. Trigg, vol. 15, pp. 185–214. New York: VCH.

Brey, W. S. (1978). Physical Chemistry and Its Biological Applications. New York: Academic Press

Bridgman, P.W. (1961). The Nature of Thermodynamics. New York: Harper & Row.

Brooks, D. R. & Wiley, E. O. (1988). Evolution as Entropy, 2nd edn. Chicago: University of Chicago Press.

Cantor, C. R. & Schimmel, P. R. (1980). Biophysical Chemistry, vols. I, II and III. San Francisco: W. H. Freeman.

Christensen, J. J., Hansen, L. D. & Izatt, R. M. (1976). Handbook of Proton Ionization Heats and Related Thermodynamic Quantities. New York: John Wiley.

Introduction

Thus far our principal concern has been fairly well established aspects of energy transformation in living organisms, the macromolecules they're made of, and the environments in which living things flourish. There has been a decidedly practical slant to much of the discussion to show how concepts from thermodynamics are useful in today's biochemistry laboratory. In the present chapter, we'll change tack and set sail for waters less well charted. The exploration will aim to locate the material covered thus far in the broader scheme of things, and also to see how the development of topics of considerable current interest must conform somehow, probably, to laws of thermodynamics. Our course might be somewhat off the mark, as the questions we wrestle with here are more speculative than above; often, no right answer is known. But the journey will not be any less worth the effort, as it will help to reveal how lively a subject biological thermodynamics is today and draw attention to a few of the areas where there is still much work to be done. An undercurrent of the discussion is a research program proposed over a century ago by the great British physicist Lord Kelvin: (1824–1907) to explain all phenomena of the world, both natural and manmade, in terms of energy transformations. The absolute temperature scale we have used throughout this book to quantify thermal energy is named in Kelvin's honor.

The computer program IRATE calculates intrinsic rates of hydrogen exchange for all backbone amide hydrogens in a given amino acid sequence, using the method of Bai et al. (1993) Proteins, 17, 75–86. The input file must be an ASCII file and the amino acid sequence must be in single letter code. The program accepts both upper case or lower case letters, but the input file must not contain spaces.

Introduction

The Gibbs free energy is important in biology research because it enables one to predict the direction of spontaneous change for a system under the constraints of constant temperature and pressure. These constraints generally apply to all living organisms. In the previous chapter we discussed basic properties of the Gibbs free energy, showed how its changes underlie a number of aspects of physical biochemistry, and touched on what the biological scientist might do with such knowledge. Here, we build on the introductory material and explore how it can be applied to a wide variety of topics of interest to the biological scientist. A range of examples illustrate when, where, why, and how the Gibbs free energy is such a useful concept. We shall discuss the energetics of different types of biological structure, including small organic molecules, membranes, nucleic acids, and proteins. This will help to give a deeper sense of the relatedness of some seemingly very different topics one encounters in biological science.

Photosynthesis, glycolysis, and the citric acid cycle

This section presents a low-resolution view of the energetics of photosynthesis, glycolysis, and the citric acid cycle. There can be no doubt that the details we omit are important: entire books have been written on each subject! But our aim here is to consider biological energy in a global, qualitative way. We want to try to see “the big picture.”

Introduction

Classical thermodynamics provides a phenomenological description of nature, and then only some aspects of nature. The mathematical relationships of thermodynamics are precise, but they do not tell us the molecular origin of the properties of matter. This chapter discusses a means of gaining a molecular interpretation of thermodynamic quantities. If you've spotted the trend we set from page one of this book, you will guess that mathematics will play an important role here. The required mathematical ability is greater than in pages past, but not greatly so. As before, all the main ideas can be expressed relatively clearly in figures or easily in words. And it is important to be able to use the mathematics, even if it is more important to the biochemist to have a good sense of what the mathematics says! We could say that this is what distinguishes the biochemist from the mathematician. It may be that mathematics applies to everything, and it may be that few things are as sublime or beautiful as Leonhard Euler's contributions to number theory, but with apologies to Thomas Alva Edison, it is the physical biochemist who hires the mathematician, not the mathematician who hires the physical biochemist.

The need for working out a theory of thermodynamics grew increasingly evident as the work of British chemist and physicist John Dalton (1766–1844) and Russian chemist Dmitri Ivanovich Mendele'ev (1834–1907) on the atomic theory of matter became more generally accepted after the middle of the nineteenth century.