Microcalorimetry of Macromolecules E-Book

Peter L. Privalov

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 549

Veröffentlichungsjahr: 2012

Beschreibung

Examining the physical basis of the structure of macromolecules--proteins, nucleic acids, and their complexes--using calorimetric techniques Many scientists working in biology are unfamiliar with the basics of thermodynamics and its role in determining molecular structures. Yet measuring the heat of structural change a molecule undergoes under various conditions yields information on the energies involved and, thus, on the physical bases of the considered structures. Microcalorimetry of Macromolecules offers protein scientists unique access to this important information. Divided into thirteen chapters, the book introduces readers to the basics of thermodynamics as it applies to calorimetry, the evolution of the calorimetric technique, as well as how calorimetric techniques are used in the thermodynamic studies of macromolecules, detailing instruments for measuring the heat effects of various processes. Also provided is general information on the structure of biological macromolecules, proteins, and nucleic acids, focusing on the key thermodynamic problems relating to their structure. The book covers: * The use of supersensitive calorimetric instruments, including micro and nano-calorimeters for measuring the heat of isothermal reactions (Isothermal Titration Nano-Calorimeter), the heat capacities over a broad temperature range (Scanning Nano-Calorimeter), and pressure effects (Pressure Perturbation Nano-Calorimeter) * Two of the simplest but key structural elements: the alpha and polyproline helices and their complexes, the alpha-helical coiled-coil, and the pyroline coiled-coils * Complicated macromolecular formations, including small globular proteins, multidomain proteins and their complexes, and nucleic acids * Numerous examples of measuring the ground state of protein energetics, as well as changes seen when proteins interact The book also reveals how intertwined structure and thermodynamics are in terms of a macromolecule's organization, mechanism of formation, the stabilization of its three-dimensional structure, and ultimately, its function. The first book to describe microcalorimetric technique in detail, enough for graduate students and research scientists to successfully plumb the structural mysteries of proteins and the double helix, Microcalorimetry of Macromolecules is an essential introduction to using a microcalorimeter in biological studies.

Leseprobe

Table of Contents

Cover

Title page

Copyright page

1 INTRODUCTION

2 METHODOLOGY

2.1. THERMODYNAMIC BASICS OF CALORIMETRY

2.2. EQUILIBRIUM ANALYSIS

2.3. AQUEOUS SOLUTIONS

2.4. TRANSFER OF SOLUTES INTO THE AQUEOUS PHASE

3 CALORIMETRY

3.1. ISOTHERMAL REACTION MICROCALORIMETRY

3.2. HEAT CAPACITY CALORIMETRY

3.3. PRESSURE PERTURBATION CALORIMETRY

4 MACROMOLECULES

4.1. EVOLUTION OF THE CONCEPT

4.2. PROTEINS

4.3. HIERARCHY IN PROTEIN STRUCTURE

4.4. NUCLEIC ACIDS

5 THE α-HELIX AND α-HELICAL COILED-COIL

5.1. THE α-HELIX

5.2. α-HELICAL COILED-COILS

5.3. α-HELICAL COILED-COIL PROTEINS

6 POLYPROLINE-II COILED-COILS

6.1. COLLAGENS

6.2. CALORIMETRIC STUDIES OF COLLAGENS

6.3. THERMODYNAMICS OF COLLAGENS

7 GLOBULAR PROTEINS

7.1. DENATURATION OF GLOBULAR PROTEINS

7.2. HEAT DENATURATION OF PROTEINS

7.3. COLD DENATURATION

7.4. pH-INDUCED PROTEIN DENATURATION

7.5. DENATURANT-INDUCED PROTEIN UNFOLDING

7.6. UNFOLDED STATE OF PROTEIN

8 ENERGETIC BASIS OF PROTEIN STRUCTURE

8.1. HYDRATION EFFECTS

8.2. PROTEIN IN VACUUM

8.3. BACK INTO THE WATER

9 PROTEIN FOLDING

9.1. MACROSTABILITIES AND MICROSTABILITIES OF PROTEIN STRUCTURE

9.2. PROTEIN FOLDING TECHNOLOGY

9.3. FORMATION OF PROTEIN STRUCTURE

10 MULTIDOMAIN PROTEINS

10.1. CRITERION OF COOPERATIVITY

10.2. PROTEINS WITH INTERNAL HOMOLOGY

11 MACROMOLECULAR COMPLEXES

11.1. ENTROPY OF ASSOCIATION REACTIONS

11.2. CALORIMETRY OF ASSOCIATION ENTROPY

11.3. THERMODYNAMICS OF MOLECULAR RECOGNITION

12 PROTEIN–DNA INTERACTION

12.1. PROBLEMS

12.2. BINDING TO THE MAJOR GROOVE OF DNA

12.3. BINDING TO THE MINOR GROOVE OF DNA

12.4. COMPARATIVE ANALYSIS OF PROTEIN–DNA COMPLEXES

12.5. CONCLUDING REMARKS

13 NUCLEIC ACIDS

13.1. DNA

13.2. POLYNUCLEOTIDES

13.3. SHORT DNA DUPLEXES

13.4. RNA

Index

Copyright © 2012 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data

9781118104514

1

INTRODUCTION

Talking and contention of Arguments must soon be turned into labours; all the fine dreams of Opinions and universal metaphysical natures, which the luxury of subtle brains has devised would quickly vanish and give place to solid Histories, Experiments and Works.

Hooke (1665)

The microcalorimetry of biological molecules is attracting increasing attention for several reasons. First, it was finally realized that proteins and nucleic acids, consisting of thousands of atoms participating in thermal motion, represent individual quasi-macroscopic systems. Correspondingly, they are usually called macromolecules. As with other macroscopic systems, understanding individual macromolecules requires knowledge of their thermodynamics, since that determines their most general properties.

Second, the thermodynamics of biological macromolecules is expected to be very abnormal because of the unusual spatial organization of these objects: every atom in their structure occupies a definite place, as in a crystal—but in contrast to a crystal these macromolecules have no symmetry and no periodicity in the disposition of their atoms. Such ordered aperiodic macroscopic systems have never before been dealt with in physics. Therefore, one cannot a priori predict the thermodynamic properties of biological macromolecules. In consequence, without knowing their thermodynamics one cannot engineer new macromolecules with defined properties. Without knowledge of their energetic basis, all discussion of the principles of organization of these macromolecules, of the mechanism of their formation and the stabilization of their three-dimensional structure, and therefore of their function (which assumes certain rearrangements of their structure), is mere speculation. This has become apparent only after many years of unsuccessful attempts to solve these problems by just analyzing the known structures of macromolecules. This failure has made it clear that structural information represents only one facet of a macromolecule; the other facet is its energetic basis, that is, its thermodynamics. These two fundamental information sets cannot be deduced from one another: each has to be obtained experimentally using very different methods.

Third, new and efficient experimental methods have been developed to obtain the necessary thermodynamic information on individual macromolecules in solution. Of special importance has been the development of supersensitive calorimetric instruments, isothermal reaction and heat capacity microcalorimeters, for studying the thermodynamic properties of biological macromolecules to measure the energetic bases of these molecular constructs. These properties of individual macromolecules need to be studied in highly dilute solutions—using, moreover, minimal quantities of these expensive objects: this has required especially sensitive and precise instruments.

In this book we start by reminding readers of the basics of thermodynamics useful for calorimetry and by giving relevant physicochemical information on the aqueous solutions of organic compounds. Then we describe the calorimetric techniques used for thermodynamic studies of biological macromolecules: the instruments for measuring the heat effects of various processes, namely, the heats of isothermal reactions between various reagents, the heats of temperature-induced changes in the samples being studied, that is, the heat capacities at constant pressure, and the heats associated with the pressure-induced changes at constant temperature. Calorimetry is a classical method that has been used extensively in science for a long time. However, studies of the thermodynamics of biological macromolecules, which are available in very limited amounts and can be studied only in highly dilute solutions, required development of supersensitive calorimetric instruments—microcalorimeters and even nanocalorimeters—to measure heats of isothermal reaction (isothermal titration nanocalorimeter), heat capacities over a broad temperature range (scanning nanocalorimeter), and pressure effects (pressure perturbation nanocalorimeter). Chapter 3 gives advice on how to use these techniques effectively in experiments with biological macromolecules, that is, proteins, nucleic acids, and their complexes.

Chapter 4 condenses general information on the structure of biological macromolecules—proteins and nucleic acids—to focus attention on the key thermodynamic problems relating to their structure. The results of calorimetric studies of various types of biological macromolecules and their complexes are then considered in the following chapters. We start from the two simplest, but highly important and far from fully understood, structural elements: the α and polyproline helices and their complexes, the α-helical coiled-coil and the polyproline coiled-coils. We then continue with more complicated macromolecular formations: small globular proteins; multidomain proteins and their complexes, particularly with DNA; and finally nucleic acids themselves. As will be seen, these calorimetric studies have led to serious reconsideration of many widely accepted dogmas concerning the roles of hydrogen bonding, hydrophobic interactions, and water in the formation of macromolecular structures.

Finally, I thank all my collaborators who worked with me during almost half a century on creation of a new experimental technique, microcalorimetry, and developing with such instruments a new field in experimental biophysics—the energetics of biological macromolecules. Among my numerous collaborators I have to mention particularly Vincent Cavina, Colyn Crane-Robinson, Anatoly Dragan, Vladimir Filimonov, Ernesto Freire, Hans Hinz, Nick Khechinashvili, George Makhatadze, Leonid Medved, Jamlet Monaselidze, Valery Novokhatni, Valerian Plotnikov, Wolfgang Pfeil, Sergei Potekhin, George Privalov, Oleg Ptitsyn, Rusty Russel, Tamara Tsalkova, and Paul Vaitiekunas. I have to mention specially my late friends who stimulated my involvement in studying the thermodynamics of biological macromolecules: Chris Anfinsen, John Edsall, Stanley Gill, Julian Sturtevant, and Jeffries Wyman.

I thank Thermo Analytical Instruments for their excellent manufacture of the calorimeters designed by my group and for providing photos of their parts for this book. The availability of these supersensitive instruments, nanocalorimeters, has opened a wide prospect for the experimental investigation of the thermodynamics of biological macromolecules and their complexes.

2

METHODOLOGY

2.1. THERMODYNAMIC BASICS OF CALORIMETRY

2.1.1. Energy

Energy is one of the most abstract notions. The energy conservation law is one of the greatest generalizations in science:

Energy does not disappear or appear; it only changes its form and appears in the form of mechanical energy, thermal energy, electrostatic energy, and so on.

We cannot sense energy, cannot measure it directly, but can only judge it by the manifestation of its changes, which appear in the forms of work (W) done and heat (Q) evolved:

 (2.1)

In the case of chemical reactions, particularly those involving proteins and those connected with changes of protein structure, the mechanical work done is associated with the change of volume ΔV of the system being considered; at constant external pressure P this is

 (2.2)

If the volume of a system decreases under the process being considered (i.e., the system is compressed under external pressure), then the work done on the system is positive, and the energy of the system increases:

 (2.3)

2.1.2. Enthalpy

Rewriting Equation (2.3) as

 (2.4)

it appears that the heat provided to the system changes its energy and does the work. This heat could be regarded as some invisible liquid substance that is poured into the system—for a long time heat was regarded as a liquid substance, phlogiston. It was assumed that the phlogiston poured into a system raised the heat content of a system. The heat content of a system is called enthalpy and is designated by the symbol H. Thus, in providing heat to the system we are increasing its enthalpy:

 (2.5)

Enthalpy is the energy of the extended system: it includes not only the internal energy of a system itself (ΔE) but also the energy of its surroundings; that is, it also includes the external work (P ΔV) that is done by the system or is performed on the system by its surroundings.

Since the systems with which we usually deal are in some environment, it is clear that all changes of such systems are associated with a change of this extended energy, the enthalpy. The change of enthalpy of a system is measured by the heat that is released or absorbed by the system under the process being considered. This is just what calorimetry does: measuring the heat of reaction determines the enthalpy change of the system in which the reaction takes place.

2.1.3. Temperature

Temperature is a measure of the warmth or coldness of an object with reference to some standard value. The temperature of two macroscopic systems is the same when the systems are in thermal equilibrium. There is no heat flow between the systems when they are in equilibrium, and the heat flow between them increases with increasing difference in temperature between these systems, flowing from the warmer to the cooler system.

Temperature does not depend on the size of the system; it is an intensive characteristic of the thermal state of any macroscopic system.

There are several scales for temperature. The most popular in the United States, the Fahrenheit scale, is the vaguest because it does not have clear reference temperatures: 0°F is the freezing point of mercury and 100°F is the physiological temperature of a human, which certainly is not a good reference because different parts of the body have different temperatures. Much better and more practical is the Celsius scale because it has clear reference points: 0°C is the temperature of water freezing at normal pressure, that is, at 1 atmosphere (1 atm = 1 kg/cm2 = 9.8 N/cm2); 100°C is the temperature of water boiling at normal pressure. This scale has particular importance for biology since liquid water is a natural internal component of all living systems. The most appropriate for science is the absolute scale, or the Kelvin scale, because this scale has a clear physical meaning: at 0 K all thermal motions are frozen—the system is at the lowest energy level. In this scale the temperature appears as an absolute characteristic of the intensity of thermal motion of the atoms constituting the macroscopic object. Therefore, the Kelvin scale is the only scale that can be used in thermodynamic analysis.

The units of temperature (degrees) in the Celsius and Kelvin scales are identical and are designated as °C or as K, respectively. Denoting temperature in the Kelvin scale by °K is incorrect. The temperature 0°C corresponds to 273.16 K, and 0 K corresponds to −273.16°C. Temperature difference in the Celsius scale is also expressed in kelvins (the unit K); thus the difference between T2 = 37°C and T1 = 25°C is 12 K, but not 12°K or 12°C.

2.1.4. Energy Units

The heat effect, that is, the amount of thermal energy, is measured in calories. One calorie is the amount of heat necessary to raise the temperature of one gram of water from 14.5°C to 15.5°C. Calories are useful for measuring heat in practical life and in biology because of the dominant role of water in our external and internal media. However, the calorie is not a practical unit for measuring energy in science, particularly in the physical sciences. The International Union of Pure and Applied Chemistry (IUPAC) recommends using the joule as the energy unit in science.

Joule (J)is the unit of work done by a force of one newton when its point of application moves through a distance of one meter in the direction of the applied force.

Newton (N)is the unit of force that produces an acceleration of one meter per square second when applied to a mass of one kilogram.

The joule is about 4 times smaller a unit of energy than the calorie:

In atomic physics a much smaller unit of energy, the erg, is used:

Ergis the work of 1 dyne of force applied over the distance of one centimeter.

Dyneis the unit of force that produces an acceleration of one centimeter per square second on a mass of one gram.

In biological physical chemistry the erg is not used because it is too small a unit of energy.

2.1.5. Heat Capacity

The amount of heat needed to heat a body from temperature T1 to temperature T2 depends on a thermal property of the body called the heat capacity. The heat capacity of a body is determined by the amount of heat that is required to increase its temperature by 1 K. If the body is heated at constant volume, the heat provided to the body will be used to increase its internal energy. Correspondingly, the heat capacity at constant volume is

 (2.6)

If the body is heated at constant pressure, its heating would be associated with thermal expansion, that is, with the external work. Therefore in that case the heat capacity is determined by the change of the enthalpy of the system when its temperature is increased by 1 K:

 (2.7)

The heat capacity at constant pressure is a more important characteristic than the heat capacity at constant volume because direct measurement of the heat capacity of solid or liquid bodies at constant volume is impossible due to their thermal expansion.

Heat capacity is an extensive characteristic of a body because it is proportional to the body’s size (i.e., its mass):

 (2.8)

The coefficient of proportionality, cp, is called specific heat capacity.

Specific heat capacity is an intensive characteristic of the material constituting a body since it does not depend on the body’s size.

It is determined by the amount of heat (i.e., the amount of enthalpy) required to raise the temperature of 1 g of material by 1 K.

The unit of specific heat capacity is joules per kelvin per gram (written J/K·g or J·K−1·g−1). The heat capacity also can be specified per mole of substance; in that case it is called a molar heat capacity and is expressed as joules per kelvin per mole (written J/K·mol or J·K−1·mol−1). The sequence of these symbols is important. To write J/mol·K is incorrect because J/mol does not have the meaning of heat capacity.

Usually the heat capacity is a temperature-dependent function:

 (2.9)

Integrating this expression from temperature T1 to T2, one gets

Rearranging this, we get

or

 (2.10)

Thus, if we know the enthalpy of a system at temperature T1 and the heat capacity of this system in the whole temperature range from T1 to T2, we can estimate what the enthalpy of this system would be at temperature T2. If the heat capacity does not depend on temperature, we simply have

 (2.11)

2.1.6. Kirchhoff’s Relation

Consider the following process: heat the system in state A from temperature T1 to Tt. At temperature Tt some transformation of this system (e.g., melting) takes place, with its state changing from A to B. This transformation is accompanied by the change in heat capacity

and enthalpy

What will the enthalpy of the system be at temperature T2?

 (2.12)

If T1 = T2 = T, then

and

 (2.13)

If , then

 (2.14)

Thus, if we know the enthalpy of the reaction at some temperature T2, we can calculate it for any other temperature T (Fig. 2.1). All we need to know are the heat capacities of the initial and final states in the temperature range being considered.

Figure 2.1. If the enthalpy of a reaction at some temperature Tt is known, one can calculate it for any other temperature T using the difference between the heat capacities of the initial and final states.

If T2 = T1 + δT and T2 − T1 = δT, then ΔH(T2) − ΔH(T1) = δΔH(T) and δΔH(T) = ΔCp × δT, or

 (2.15)

This is the Kirchhoff relation, which means the following:

If the heat capacity increases upon some reaction, the enthalpy of the reaction is an increasing function of temperature and vice versa—if the enthalpy of reaction is an increasing function of temperature, this means that the heat capacity of the final state is larger than the heat capacity of the initial state.

2.1.7. Entropy

The entropy of a system represents the part of the energy of a system that has been dissipated in thermal motion. Therefore, the entropy can be considered as a measure of a system’s disorder. According to the second principle of thermodynamics:

All processes in an isolated system develop in the direction of an increase of its entropy, that is, of raising its disorder.

In contrast to enthalpy, the change in the entropy of a system in some reaction is determined by the heat Q that is received by the system, divided by the absolute temperature at which the reaction takes place:

 (2.16)

If we want to determine the change in entropy of a system upon heating from T1 to T2, we have to integrate the following equation:

 (2.17)

According to the third principle of thermodynamics:

At absolute zero temperature (0 K) the entropy of all macroscopic systems is zero; that is, the systems are in complete order.

Therefore, for the absolute entropy of a system at any other temperature we have

 (2.18)

The absolute entropy of a system is an absolute measure of the system’s disorder. However, measurement of the heat capacity function of an object from absolute zero temperature to room temperature is not easy. It is especially difficult for aqueous solutions, which freeze below 273 K with large decrease in entropy. Also the entropy of an aqueous solution at 0 K does not become zero because water at that temperature still has residual disorder from the undetermined location of its two protons between two possible positions for each. Therefore, the absolute entropy of aqueous solutions cannot be determined. Because of that, in considering aqueous solutions the standard entropy is usually used, choosing some state as a reference.

Suppose we know that upon heating a system changes state from A to B at the transition temperature Tt, and this results in a change of entropy ; the heat capacities of the initial and final states are Cp(T)A and Cp(T)B. What will the entropy of this system be at temperature T compared with its entropy at temperature Tt?

We have

 (2.19)

If T = T1,

 (2.20)

If ,

 (2.21)

This shows that the entropy of a reaction is a function of temperature and depends on the sign of the heat capacity difference between the final and initial states, ΔCp.

If ΔCp > 0, then the entropy of reaction is an increasing function of temperature. If ΔCp < 0, then the entropy is a decreasing function of temperature.

The unit of entropy is joules per kelvin (J/K) or calories per kelvin (cal/K); the latter is also called the entropy unit and is designated simply as “e.u.” Correspondingly, the molar entropy is expressed in joules per kelvin per mole (J/K·mol) or calories per kelvin per mole (cal/K·mol) and the specific entropy in joules per kelvin per gram (J/K·g) or calories per kelvin per gram (cal/K·g), which can be also written as J·K−1·g−1 and cal·K−1·g−1. In the case of proteins it could be also expressed per mole of amino acid residues, J/K·(mol-res) or cal·K−1·(mol-res)−1; in the case of nucleic acids the specific entropy could be expressed per mole of base pairs, that is, J/K·(mol-bp) or cal/K·(mol-bp).

2.1.8. Gibbs Free Energy

Change of the Gibbs free energy, ΔG, shows the part of the energy of an extended system that can be converted into work at a constant temperature.

Since

we have the following for the Gibbs energy:

 (2.22)

The Gibbs free energy is a very important function because it determines the equilibrium constant for any reaction:

 (2.23)

Correspondingly, the Gibbs energy of reaction can be determined from the equilibrium constant:

 (2.24)

Here R is the universal gas constant: R = 2.0 cal/K·mol = 8.31 J/K·mol (or 8.31 JK−1·mol−1).

2.2. EQUILIBRIUM ANALYSIS

2.2.1. Two-State Transition

Thermodynamics of some process in a system occurring upon a variation of conditions is more or less easily described if the observed changes are due to transitions between two definite states of the system. In this case, and only in this case, all the observed effects can be specified through the equilibrium constant:

 (2.25)

where θa and θb are values of any observed indices characterizing the initial and final states of the system being considered under the given conditions. Studying the dependence of equilibrium constant on external variables (such as temperature, pressure, and ion activity) one can derive the effective parameters characterizing the process.

Consider equilibrium of two phases at the temperature of the phase transition, Tt. In the case of a monomolecular reaction the equilibrium constant is determined by the ratio of the fractions of the molecules in the final and initial states:

 (2.26)

where K = 1 at the temperature of the transition midpoint, Tt. Bearing in mind Equation (2.24), we have that at the transition midpoint ΔG(Tt) = 0. This means that at the transition temperature the transfer from one phase to another does not lead to a gain or loss of energy—no work is done. Then, since

we get the following for temperature Tt:

 (2.27)

It is important that T be given in the absolute scale.

Thus, we can determine the entropy at the transition temperature just by measuring the heat effect of a transition, that is, the enthalpy of a transition. If we know the heat capacity of the initial state and of the final state, that is, the difference of these heat capacities ΔCp, then we can determine the entropy difference of two phases at any other temperature:

 (2.28)

If ΔCp does not depend on temperature, then

 (2.29)

2.2.2. Derivatives of the Equilibrium Constant

The equilibrium constant of any transition depends on the intensive variables determining the environmental conditions, particularly temperature (T), pressure (P), and ligand activity (a).

If in the monomolecular two-state transition A ⇔ B only the temperature is variable and the pressure and ligand activity are constant, then, bearing in mind that

 (2.30)

and

 (2.31)

we have the following for the temperature derivative of the equilibrium constant:

 (2.32)

However, since

and

we get

 (2.33)

This is called the van’t Hoff equation. It can be rewritten as

 (2.34)

Thus, analyzing the temperature dependence of the equilibrium constant of a reaction, one can determine the enthalpy of the reaction. This enthalpy is usually called the van’t Hoff enthalpy or the effective enthalpy because it is valid only if the reaction represents a two-state transition.

To get the value of the van’t Hoff enthalpy, ln K is plotted against 1/T. The slope of this function is equal to

If the function thus obtained is linear, the enthalpy does not depend on temperature; if it has noticeable curvature, the enthalpy depends on temperature; that is, the reaction proceeds with heat capacity change.

When pressure is a variable parameter in a reaction, bearing in mind that ΔH = ΔE + P ΔV and ΔG = −RT ln K = ΔH − T ΔS = ΔE + P ΔV − T ΔS, one finds

 (2.35)

Thus, analyzing the dependence of the logarithm of the equilibrium constant on pressure, at constant temperature and ligand concentration, one finds the volume effect of the reaction.

If the variable parameter is ligand concentration, bearing in mind that

 (2.36)

one finds

 (2.37)

At low concentration of a ligand its activity is close to its molar concentration. Therefore, analyzing the dependence of the logarithm of the equilibrium constant on the logarithm of ligand concentration, one can determine the quantity of bound or released ligand in a process.

2.3. AQUEOUS SOLUTIONS

2.3.1. Specificity of Water as a Solvent

Water represents a universal averment for all biological species and a unique solvent for its components, particularly proteins and nucleic acids. The specificity of water proceeds from its very particular structure: The two hydrogens of water and two lone electrons form a highly polar tetrahedron (Fig. 2.2). Therefore water has two hydrogen donors and two hydrogen acceptors: the hydrogen acceptors are the two lone electrons; the role of donor is played by the oxygen, which has two covalently bound hydrogens. As a result, in ice each water molecule forms four hydrogen bonds with four of its neighbors (Fig. 2.3).

Figure 2.2. The electronic structure of a water molecule.

Figure 2.3. The structure of normal ice.

An important property of the water molecule is cooperativity in formation of hydrogen bonds:

Formation of one hydrogen bond with a neighboring water molecule increases the probability of formation of a bond with another neighbor because it increases the electronegativity of the acceptor groups.

The ability to form four hydrogen bonds, and cooperativity in their formation, results in unique properties of water: it is a liquid with high tendency to have an ordered structure. The structure of water below 0°C (i.e., of ice) is rather open, transparent, with large cavities. Density of ice is significantly lower than that of liquid water. But even above 0°C, water molecules have a tendency to form an icelike structure. Therefore, water represents a highly structured liquid. The combination of “liquid” and “structured” sounds like a paradox. This structure, however, is not fixed; it largely fluctuates. Thus, its orderliness appears as flickering clusters of the icelike structure. With temperature increase the average amount of the ordered clusters decreases. It appears as if they melt gradually and this results in a very high heat capacity of water. The heat capacity of water is almost 3 times higher than that of organic liquids.

Due to its polarity water forms hydrogen bonds with all polar solutes and strongly interacts with charged molecules. Correspondingly, polar and charged molecules are highly soluble in water. Because of the high polarity of the water molecule, liquid water has a very high dielectric constant, 78. Therefore, water efficiently screens electrostatic interaction between charged groups and promotes dissociation of ionic pairs, particularly dissociation of the removable hydrogen in acids.

2.3.2. Acid–Base Equilibrium

The acid–base properties of any substance in aqueous solution are connected with the presence of a removable proton. We call a substance an acid if it tends to release its proton and a base if it tends to accept a proton. The structure B, which remains after a hydrogen ion is removed from the acid BH, represents the base conjugate to the acid:

 (2.38)

Since the hydrogen ion is positively charged, it is clear that either the BH or B, or both, must be electrically charged, and that the charge on B must be more negative (or less positive) than that on BH by one proton unit. If the net charge of BH is Z, then the charge of B is Z − 1.

 (2.39)

The equilibrium constant of Reaction (2.38) is

 (2.40)

where aH, aB, and aBH are the corresponding activities.

Replacing activities by concentrations, since at low concentrations they do not differ much, one gets

 (2.41)

In the case of water, we have

 (2.42)

The hydrogen ion (proton) is extremely reactive. It immediately joins another water molecule, forming the hydronium ion, H3O+.

Concentrations of H+ and OH− in pure water are equal and very low, 10−7 M. This is usually presented in a logarithmic scale: log([H+]) = −7.0. Here [H+] is the dimensionless relative concentration of protons [H+]/[H+]0, where [H+]0 = 1 M is a standard concentration of protons. The “−log” is usually denoted as “p”; therefore −log([H+]) = pH.

The pH of the neutral aqueous solution is 7.0. In this notation, Reaction (2.42) can be rewritten as

 (2.43)

Let α be the fraction of the deprotonated form B:

 (2.44)

Correspondingly, the fraction of the protonated form is

 (2.45)

and Equation (2.43) appears as

 (2.46)

This can be rewritten as

 (2.47)

It shows that when pH = pK, then α = 1/2; when pH  pK, then α decreases to 0; when pH  pK, then α approaches 1.0. Figure 2.4 illustrates this for titration of the amino acid glycine. This amino acid has two titratable groups: the α-carboxy, with pK = 2.4; and the α-amino, with pK = 9.8. At low pH both groups are protonated and the molecule has one positive charge. With increasing pH, that is, decreasing hydrogen concentration in the solution, first the α-carboxy group starts to deprotonate, becoming negatively charged. Therefore, at neutral pH glycine has one positive and one negative charge. With further increase of pH (decrease of hydrogen concentration), the α-amino group deprotonates, that is, loses its positive charge, and the molecule becomes negatively charged.

Figure 2.4. Deprotonation of glycine at increasing pH.

The work required to remove hydrogen is expressed by the Gibbs energy of this reaction:

 (2.48)

For the reaction BH ↔ B− + H+, −ln K = −2.3 log K = 2.3 pK, and we have

 (2.49)

Using this equation one finds that at room temperature (25°C = 298.15 K) removal of the first hydrogen from glycine costs ΔGI = 8.36 × 298.15 × 2.4 kJ/mol = 6.0 kJ/mol; the second hydrogen costs ΔGII = 24.4 kJ/mol. Thus, the α-amino group holds onto the extra hydrogen much more strongly than the α-carboxyl group. The thermodynamic characteristics of protonation of the most common groups in proteins are listed in Table 2.1.

TABLE 2.1. Thermodynamic Characteristics of Deprotonation of Protein Groups at 25°C

2.3.3. Partial Quantities

In biochemistry, molecular biology, and physical chemistry of biopolymers, we usually deal with aqueous solutions, and mostly with rather dilute solutions. However, we are particularly interested in the properties of individual components in the solution. Separation of the properties of a certain component from the overall properties of the solution is not a simple problem because interactions between the solute components of the solution are not simple. However, at low concentrations, where interactions between the solute molecules are negligible, their contribution to the overall properties of the solution is defined by the partial characteristic of a component. In particular, in the case of heat capacity, the partial heat capacity of the ith component is defined as a change in the total heat capacity of a unit mass of solution upon addition of component i at a constant concentration of all other components j:

 (2.50)

The heat capacities of a series of solutions, in which only the concentration of the ith component ωi is varied, are measured and plotted against ωi; by extrapolating the slope of this function to low concentrations, the partial heat capacity of the ith component is determined. However, if the heat capacity of a macromolecular solution is measured at concentrations less than 0.1%, the partial heat capacity of the solute can be determined just by comparing the heat capacity of the solution with the heat capacity of the solvent (see Section 3.2.3). Figure 2.5 presents examples of the calorimetric determination of partial molar heat capacity of linear alcohols.

Figure 2.5. The calorimetrically measured partial molar heat capacity of linear alcohols (Makhatadze et al., 1997).

Combinatorial analysis of the partial molar heat capacities of various linear molecules led to understanding that the contribution of various groups to the overall heat capacity of the compound is additive and quite definite (Fig. 2.6). It showed that the contribution of the nonpolar group to the overall heat capacity of the molecule is positive and decreases with increasing temperature, in contrast to the contribution of the polar and charged groups, which decreases with decreasing temperature and even changes sign at low temperatures, becoming negative (Makhatadze and Privalov, 1988, 1989, 1990; Murphy and Gill, 1991; Livingstone et al., 1991; Spolar et al., 1989, 1992).

Figure 2.6. Temperature dependence of the partial molar heat capacities of (a) –CH3, (b) , (c) –OH, (d) –COOH, (e) –CONH2, (f) groups (Makhatadze and Privalov, 1990).

2.4. TRANSFER OF SOLUTES INTO THE AQUEOUS PHASE

2.4.1. Hydration Effects

Transfer of molecules from the nonaqueous phase into the aqueous phase results in hydration of these molecules. The molecules could be transferred into the liquid aqueous phase from their condensed phase, liquid phase, or gaseous phase. However:

The net hydration effects include the enthalpy, entropy, and Gibbs energy of transfer of a molecule from a fixed position in an ideal gas phase into a fixed position in water.

These can be determined from the heats of desolation of the liquid or condensed phase in water, taking into account the enthalpy and entropy of melting and vaporization of these phases (Fig. 2.7). The thermodynamic characteristics of this process do not include the effects associated with the difference in volume of the two phases, that is, the difference in the translational motion of the molecule in the phases. They do not include the interactions between the transferred molecules, but only the effects associated with the insertion of the solute molecule into solvent, usually water. The insertion of a solute molecule into water is in itself a complex process. It includes cavity formation in water, interaction of the water molecules with the inserted molecule, and reorganization of the water molecules caused by the inserted solute (Lee, 1985).

Figure 2.7. Scheme of various ways to transfer solutes into water.

The chemical potential μ of a solute in any phase can be separated into two parts: μ = μ1 + μ2, where μ1 is the work involved in inserting the solute molecule at a fixed point in the given phase, and μ2 = RT ln(Λ3ρ) is the work involved in “liberating” the molecule from the fixed point so that it can roam about entire volume of the phase. Here Λ is the momentum partition function, and ρ is the molar concentration (Ben-Naim, 1980, 1987). Because the hydration effect is associated with μ1, it follows that all experimentally obtained transfer characteristics should be corrected for the effect of liberation.

When the concentration is expressed in the molar scale, the Gibbs energy of hydration is just the energy of transfer of the solute molecule from the gaseous phase into water:

 (2.51)

where ρg and ρw are the molar concentrations of the molecules in the gaseous phase and in the water solution. For the enthalpy of hydration the correction for thermal liberation gives (Ben-Naim, 1987):

 (2.52)

where αw is the thermal expansion coefficient of water at constant pressure.

For the entropy of hydration at 25°C we have

 (2.53)

The heat capacity effect of hydration is determined as

 (2.54)

Here is the heat capacity change on transfer of the molecule from the gaseous phase into water.

Studies of dissolution of various compounds in water showed the following:

The solubility of polar and charged substances is very high (i.e., they are hydrophilic), and the Gibbs energies of their transfer are negative.

In contrast, solubility of nonpolar substances is very low (i.e., they are hydrophobic); correspondingly the Gibbs energies of their transfer into water are positive. Surprisingly, it was found that the enthalpy of transfer of nonpolar substances into water at room temperature is close to zero, which means that the entropy of their transfer should be large and negative.

The other remarkable feature of the transfer of nonpolar compounds into water is that it proceeds with positive heat capacity increment—in contrast to the transfer of polar groups, which proceeds with heat capacity decrement (Table 2.2).

TABLE 2.2. Solubility, Gibbs Energy, Enthalpy, Entropy, and Heat Capacity Increment of Transfer of a Nonpolar Substance from Pure Liquid Phase to Water at 25°Ca

It is remarkable that the heat capacity increment of transfer increases with increasing surface area of the compound, suggesting that it results from hydration. Since decrease of entropy is thermodynamically unfavorable, it was believed that water expells the nonpolar substance. This expelling action of water on the nonpolar substance was called the hydrophobic force.

Decrease of entropy induced by the presence of a nonpolar substance in water was explained by increasing microscopic “icebergs” of water around the nonpolar substance (Frank and Evans, 1945). Later, these icebergs were considered as “flickering clusters” (Frank and Wen, 1957). However, it was unclear why ordering of water in the presence of nonpolar molecules, which means increase of hydrogen bonding between water molecules, does not proceed with decreasing enthalpy. One would expect an exact compensation for the entropy and enthalpy changes that arise from water ordering, and thus this effect would contribute nothing to the hydration Gibbs energy (Lumry et al., 1982; Privalov and Gill, 1988).

2.4.2. Hydrophobic Force

The heat capacity increment with the transfer of nonpolar molecules into water seemed to confirm an assumption that the presence of a nonpolar compound increases order in the surrounding water, which with increasing temperature starts to melt gradually and the excess heat of melting appears as a heat capacity increment. It was found indeed that transfer of nonpolar substance into water results in an increase of heat capacity. This, however, means that if the enthalpy of transfer of nonpolar molecules into water is zero at room temperature, it should increase with increasing temperature. Correspondingly, if the entropy of transfer of nonpolar molecules into water is negative at room temperature, it should decrease in magnitude with increasing temperature and at some high temperature should drop to zero (Fig. 2.8). For all nonpolar molecules the entropy of transfer from liquid phase to water becomes equal to zero in a rather limited temperature range above 100°C (Privalov and Gill, 1988). However, zero entropy is a condition for the ΔG extremum:

 (2.55)

Figure 2.8. Temperature dependence of the entropy of transfer of various nonpolar substances from the pure liquid phase to water (Privalov and Gill, 1988).

Thus, at this temperature TS, the ΔG of transfer of a nonpolar substance from the liquid phase into water reaches its maximum value (Fig. 2.9). This maximal value of ΔG is provided only by the enthalpy of transfer, which is positive and large at temperature TS. This enthalpy of transfer at TS appeared to be close in value to the enthalpy of vaporization of the pure nonpolar substance; that is, it is provided by the van der Waals interaction between the nonpolar molecules in the liquid phase (Baldwin, 1986; Privalov and Gill, 1989).

Figure 2.9. Temperature dependence of the Gibbs energy of transfer for various liquid hydrocarbons to water (Privalov and Gill, 1988).

It appears that there are two temperatures of a universal nature that describe the thermodynamic properties for the dissolution of nonpolar substances (liquid hydrocarbons) into water. The first of these, TH, is the temperature at which the heat of solution is zero and has a value of approximately 20°C for a variety of nonpolar substances. The second universal temperature is TS, where the standard entropy change is zero; TS is about 140°C. The standard-state Gibbs free energy change can be expressed in terms of these two temperatures, requiring knowledge only of the heat capacity change for an individual substance:

 (2.56)

In the approximation where is constant, this equation can be integrated to yield

 (2.57)

This function is plotted in Figure 2.10a. Since at TS the entropy of transfer of nonpolar solutes from their liquid phase into water is zero and the Gibbs energy of transfer reaches its maximal value, one can conclude that, although at this temperature the nonpolar solute molecules do not induce water ordering, transfer of these substances into water is most unfavorable. It appears thus, that:

The positive Gibbs energy of transfer of nonpolar substances into water is provided by van der Waals interactions between these molecules, whereas the contribution of water ordering is negative (for details see Privalov and Gill, 1988, 1989).

Figure 2.10. Two thermodynamic representations of dissolution of a liquid hydrocarbon (benzene) into water, assuming constant heat capacity effect of hydration: (a) free Gibbs energy of transfer and underlying contributions as a function of temperature; (b) solubility function and underlying contributions as a function of ln(T). Dotted lines are shown at the respective maxima, TH and TS (Privalov and Gill, 1988).

On the other hand, Equation (2.57) can be rearranged into the following:

 (2.58)

which actually expresses the solubility of the nonpolar substance in water, since . As Figure 2.10b shows, the solubility reaches its minimal value at TH. However, one can hardly say that its minimal value results from unfavorable water ordering because at this temperature the enthalpy of van der Waals interactions between nonpolar molecules is compensated by the enthalpy of water ordering, that is, of increasing hydrogen bonding between the water molecules.

An important consequence of the fact that the van der Waals and hydration effects contribute to the hydrophobic effect with opposite signs is the biphasic character of their combined effect.

Indeed, the van der Waals interactions are short range, in contrast to the water ordering effect. It is evident, therefore, that the “hydrophobic interactions” should be attractive at a short distance and repulsive at a long distance (exceeding the size of water molecule).

It appears that this biphasic character of the hydrophobic effect might be one of the reasons for the extreme cooperativity of protein folding–unfolding process (see Section 9.2).

2.4.3. Hydration of Polar and Nonpolar Groups

Analysis of the transfer characteristics of various linear molecules led to understanding that the hydration effects are proportional to the number of groups in the molecule; that is, they are additive (Fig. 2.11). Comparing the effects of transfer of various molecules into water, where the molecules have different combinations of some groups, one can determine the contribution of an individual group to the hydration effect. As Table 2.3 shows, hydration enthalpies and entropies of polar and nonpolar groups are negative at room temperature, but they are much more negative for polar groups than for aliphatic nonpolar groups. As a result, the Gibbs energies of polar groups are negative and large in magnitude, whereas for the nonpolar groups they are small, or even positive. Correspondingly, solubility of the polar molecules in water is high (i.e., they are hydrophilic), in contrast to the solubility of nonpolar molecules in water, which is low (i.e., they are hydrophobic).

Figure 2.11. Dependence of the enthalpy of transfer from gaseous phase to water for alkanes (), alcohols (), amines (), secondary alcohols (◊), and N-substituted amines (×) on the number of groups in molecule, N−CH2− (Makhatadze and Privalov, 1993).

TABLE 2.3. Hydration Enthalpy and Gibbs Energy of Various Groups at 25°Ca

The remarkable difference between the hydration effects of polar and nonpolar groups is that, with increasing temperature, the hydration enthalpy and entropy of nonpolar groups decrease in absolute value (Fig. 2.12), whereas for polar groups they increase in absolute value (Fig. 2.13). The situation with the aromatic groups is somewhat in between (Fig. 2.14). The surface normalized hydration effects of the aliphatic and aromatic groups differ considerably both in magnitude and in their dependence on temperature. Correspondingly, the hydration effects of these compounds reach zero values at different temperatures. These temperatures are different for the enthalpy and entropy of hydration of the aliphatic and aromatic groups: for the aliphatic groups, the temperature at which hydration enthalpy becomes zero, TH, is 81°C; for the aromatic groups it is 125°C. The temperature TS at which the hydration entropy for the aliphatic groups becomes zero is 122°C; for aromatic groups it is 104°C.

Figure 2.12. Temperature dependence of the hydration enthalpy, Gibbs energy, and entropy factor for the aliphatic groups (Makhatadze and Privalov, 1995).

Figure 2.13. Temperature dependence of the hydration enthalpy, Gibbs energy, and entropy factor for the polar groups (peptide unit, –CONH−) (Makhatadze and Privalov, 1995).

Figure 2.14. Temperature dependence of the hydration enthalpy, Gibbs energy, and entropy factor for the aromatic groups (Makhatadze and Privalov, 1995).

In contrast to the enthalpy and entropy of hydration, the Gibbs energy does not depend much on temperature; that is, the temperature dependencies of the enthalpy and entropy compensate each other effectively. Most important, however, is that the Gibbs energy of hydration of polar groups is large and negative, and its absolute value increases in magnitude with decreasing temperature. Therefore, these groups are clearly hydrophilic, and their hydrophilicity increases with decreasing temperature. The Gibbs energy of hydration of aliphatic groups is positive and its absolute value decreases with decreasing temperature. These groups are therefore hydrophobic, and their hydrophobicity decreases with decreasing temperature. The Gibbs energy of hydration of aromatic groups, which have been traditionally regarded as typical hydrophobic groups, is negative, although it is much smaller in magnitude than the Gibbs energy of hydration for polar groups (Privalov and Makhatadze, 1993). Therefore, these groups cannot be classified as hydrophobic. Moreover, they can hardly be classified as nonpolar, as is usually assumed.

According to Kirchhoff’s relation, d(ΔH)/dT = ΔCp, the enthalpy dependence on temperature is determined by the heat capacity change upon reaction: it is positive for apolar groups and negative for polar groups. It appears thus that the inclusion of an apolar solute in water results in an increase of the heat capacity; the inclusion of a polar solute in water results in a decrease of the heat capacity. The question is then why the heat capacity increases upon insertion of the apolar group in water and decreases upon insertion of the polar group?

It is supposed that insertion of the polar groups into water increases order in water by enhancing the hydrogen bonding among surrounding water molecules. Therefore, the flickering clusters of ordered water are more stable in the presence of polar groups and melt less upon increasing temperature. This results in overall decrease of the solution heat capacity. The apolar groups also increase the order in water but the heat capacity effect of their presence is opposite in sign. It appears then that the water ordering in these two cases is different: the apolar groups increase the order in water by occupying the cavities in its icelike structure. One would expect then that the order in water, which is induced by the presence of nonpolar molecules, is not stable and melts gradually upon heating. This diffused heat effect appears as a heat capacity increment.

REFERENCES

Baldwin R. (1986). Proc. Natl. Acad. Sci. USA, 83, 8069–8072.

Ben-Naim A. (1980). Hydrophobic Interactions. Plenum Press, New York and London.

Ben-Naim A. (1987). Solvation Thermodynamics. Plenum Press, New York and London.

Frank H.S. and Evans M.W. (1945). J. Chem. Phys., 13, 507–532.

Frank H.S. and Wen W.Y. (1957). Discuss. Faraday Soc., 24, 133–140.

Lee B. (1985). Biopolymers, 24, 813–823.

Livingstone J.R., Spolar R.S., and Record M.T., Jr. (1991). Biochemistry, 30, 4237–4244.

Lumry R., Battisel E., and Jolicoeur C. (1982). Faraday Discuss. Chem. Soc., 17, 93–108.

Makhatadze G.I. and Privalov P.L. (1988). J. Chem. Thermodynam., 20, 405–412.

Makhatadze G.I. and Privalov P.L. (1989). J. Solution Chem., 18, 927–936.

Makhatadze G.I. and Privalov P.L. (1990). J. Mol. Biol., 213, 375–384.

Makhatadze G.I. and Privalov P.L. (1993). J. Mol. Biol., 232, 639–659.

Makhatadze G.I. and Privalov P.L. (1995). Adv. Protein Chem., 47, 307–425.

Makhatadze G.I., Lopez M.M., and Privalov P.L. (1997). Biophys. Chem., 64, 93–101.

Murphy K.P. and Gill S.J. (1991). J. Mol. Biol., 222, 699–709.

Privalov P.L. and Gill S.J. (1988). Adv. Protein Chem., 139, 191–234.

Privalov P.L. and Gill S.J. (1989). Pure Appl. Chem., 61, 1097–1104.

Privalov P.L. and Makhatadze G.I. (1993). J. Mol. Biol., 232, 660–679.

Spolar R.S., Ha J.-H, and Record M.T., Jr. (1989). Proc. Natl. Acad. Sci. USA, 86, 8382–8385.

Spolar R.S., Livingstone J.R., and Record M.T., Jr. (1992). Biochemistry, 31, 3947–3955.

3

CALORIMETRY

3.1. ISOTHERMAL REACTION MICROCALORIMETRY

3.1.1. The Heat of Mixing Reaction

In the simplest binding reaction, macromolecule M has one binding site for the ligand L:

The association constant of this reaction is

 (3.1)

where [ML], [M], and [L] are the corresponding concentrations, which in dilute solutions are close to the activities.

In considering the dissociation process

the dissociation constant is

 (3.2)

Thus, Kd = 1/Ka. Correspondingly, the dimension of Ka is M−1, and of Kd is M.

The fraction F of macromolecules with the bound ligand is

 (3.3)

The fraction of macromolecules without ligands is

 (3.4)

From Equations (3.3) and (3.4) one gets

 (3.5)

At the concentration where F = 1/2,

 (3.6)

Thus, the dissociation constant, which is the reciprocal of the association constant, is just the concentration of free ligand at which half of the macromolecules have a bound ligand and half do not. The larger the binding constant, the lower the dissociation constant—and the lower the concentration of ligand at which the half-saturation is reached.

The heat of the association reaction depends on the molar enthalpy of association ΔHa, the association constant Ka, and the ligand concentration [L]. The heat effect of binding can be positive or negative, but usually for protein–protein or protein–DNA interactions it is not large in magnitude, less than 100 kJ/mol. If Ka is large, then all ligands would be bound even at small concentrations. Therefore, to get the complete binding curve, the isotherm of reaction, we need to use a very low concentration of macromolecules. A high association constant is specific for many reactions of biological macromolecules, which requires precise recognition of the partner; for example, the binding constant of gene regulating proteins is above 108 M−1 (i.e., the dissociation constant is below 10−8 M). Correspondingly, to get a complete picture of their binding, one needs to work with very dilute solutions of macromolecules, of the order of 10−8 M. On the other hand, there are many nonspecific binding reactions, which are characterized by low binding constants. For example, the interaction of denaturants (urea or guanidine hydrochloride) with proteins is characterized by a very low binding constant. Therefore, a significant effect of these reagents on proteins is observed only in concentrated solutions. However, the solubility of denaturants is limited—less than 8 M. Therefore, to achieve a high concentration of denaturant in a solution with protein, one has to mix a comparable amount of the protein solution with the concentrated solution of the denaturant. In contrast, when the binding constant is high, we have to add a very small volume of the reagent to a large volume of protein solution and repeat that many times to get a binding isotherm. Correspondingly, for studying biopolymers two different types of reaction calorimetric instruments are needed: one that permits mixing two solutions in comparable volumes, and another that permits mixing a small portion of one solution in a large portion of another one and repeating that many times.

3.1.2. Mixing of Reagents in Comparable Volumes

There are two methods of mixing reagents in comparable volumes: batch and flow-mix.

In batch calorimeters comparable volumes of two reagents are placed in the two equal compartments of the rotating calorimetric cell and are mixed by turning this cell upside down. The heat of mixing is measured by the electric signal that is produced by the heat flowing through the Peltier element (a battery of semiconductors) to the thermostat. The main disadvantage of batch calorimeters is that the noise resulting from the rotating cell and from mixing the reagents is too high and does not reproduce well. The main reason is the air phase in the calorimetric cell—which, upon turning the cell upside-down, produces bubbles in the mixture that is formed. These bubbles induce some heat effects, which cannot be taken into account. Therefore these calorimeters are no longer much used for studying reactions with biological macromolecules.

In the flow-mix calorimeter continuous laminar flows of two reagents are mixed in the reactor (Fig. 3.1). The mixture flows through a heat exchanger with the Peltier element, which converts the heat flowing to the thermostat into an electric current that is amplified and measured. The advantage of this instrument is that the liquids being studied do not contact the gas phase and the laminar constant flow of the reagent does not produce much noise. Efficient mixing in this case requires a certain turbulence; however, the Joule heat resulting from this turbulence is rather constant and can be taken into account. The main disadvantage of the existing commercial flow-mix calorimeters is that they require quite a considerable amount of the reagents to realize their constant flow through the instrument. Nevertheless, the most thorough calorimetric study of the thermodynamics of protein interaction with urea and guanidinium chloride was done using an LKB FLOW-MIX calorimeter (Pfeil and Privalov, 1976; Makhatadze and Privalov, 1992).

Figure 3.1. Schematic of the flow-mix calorimeter. The solution of one reactant is injected continuously into the calorimetric channel by the syringe F or a peristaltic pump; syringe G injects the other reagent into the channel at a point after the first heat-measuring part A and before the second heat-measuring part B. The difference between the heat effects recorded by B and A represents the heat effect of mixing of these two solutions, which is recorded.

3.1.3. Isothermal Titration Microcalorimeter

Isothermal titration calorimeters (ITCs), which permit calorimetric titration of one reagent by another, were widely used in physical chemistry. However, the reactors of conventional titration calorimeters were of rather large volume (of the order of deciliters) needed to place a mechanical stirrer to homogenize the mixture and also to minimize the influence of the surroundings on the measured heat effect. Therefore these instruments cannot be used for studying the heats of reactions between biological molecular objects, which are available in very limited amounts. The first micro-scale modification of the ITC that could be practically used for studying biological reactions was designed by S.J. Gill (McKinnon et al., 1984) and is shown in Figure 3.2. In this differential instrument two identical cells of 0.5 mL volume are placed into the thermal equilibrator block and a few microliters of titrant are injected periodically into the reactor cell by the rotating microsyringe, which also serves as a stirrer. The heat effect of mixing thus produced is detected by the sensor (the copper–constantan battery) placed between the reactor and the thermal equilibrator block and is compared with the heat effect between the reference cell and this block. After the appearance of this first micro-ITC, several companies (Microcal, Calorimetry Science Corporation CSC, TA Instruments) started production of various modifications differing from the original mainly in the sensors, electronics, and thermostatization system used.

Figure 3.2. The first twin isothermal titration microcalorimeter, designed by Stanley Gill: (a) submarine container; (b) thermal equilibration block; (c) thermoelectric module; (d) calorimetric cell (glass bulb embedded in copper cylinder with low-melting metal); (e) electric heaters; (f) close-fitting stainless-steel tube with inside glass tube; (g) glass capillary stirrer and injection needle; (h) stainless-steel centering sleeve; (i) syringe holder; (j) microsyringe; (k) sleeve bearing assembly for syringe centering; (l) stirrer drive gear (McKinnon et al., 1984).

The operational volume of commercial ITC instruments is usually on the order of 1 mL. A smaller operational volume is not appropriate since the most critical part for an ITC experiment is not the sample volume but the concentration of the reagents, whereas decreasing the operational volume increases the optimal concentrations for the ITC experiment.

Figure 3.3 shows the construction of some important parts of the commercial Nano-ITC of TA Instruments: (a) the calorimetric block, showing the locations of the twin reaction cells within the thermostatization system; (b) the reactor cell with the syringe/stirrer inside; and (c) the block rotating syringe/stirrer and its piston, which moves stepwise to inject precise portions of the titrant into the reactor cell. Perfect thermostatization and electronics of this instrument permitted reduction of the noise level to 2.5 nW and the baseline stability to ±20 nW per hour. Other important characteristics of the instrument are its short response time and the high accuracy of the portions of reagent injected into the reactor cell. The cells are made from pure gold, which is the best material for calorimetric cells not only because of its high chemical inertness but also because of its high thermal conductivity, which is important for the temperature uniformity in the cell. Figure 3.4 shows the Nano-ITC of TA Instruments.

Figure 3.3.